Math Is Fun Forum

Hey guys, sorry im quite new to mathsisfun.com I just had a simple question.

This is really going to sound pathetic and its really like grade 1 maths but for the life of me I cannot figure out the proof of this formula.Here is the proof:

  Geometric Progression = a + ar + ar^2 + ar^3 + ... + ar^n-1  (1)

  multiply formula (1) by r:    r.GP = ar + ar^2 + ar^3 + ... + ar^n-1 + ar^n (2)

  subtracting formula (2) from (1)gives: GP- r.GP = a -ar^n
 
  factoring on both sides gives: GP(1-r)=a(1-r^n)

  dividing by (1-r): GP= a(1 -r^n)/ (1-r)

My problem in the proof is not the logic behind it its the mechanics of the maths in line 2 of the proof where formula 1 gets multiplied through by r, for the life of me I dont understand why by multiplying through by "r" it leaves the term "ar^n-1". I though by multiplying the term ar^n-1 in the first formula it leaves ar^n due to the laws of exponents thus I do not see where the original term comes from in the second line. Its probably one of the most fundamental laws of algebra and I feel really bad not being able to get it, I just would really like some help on it please.

P.S. I got the proof from this url http://www.mathcentre.ac.uk/resources/workbooks/mathcentre/APGP.pdf page 9 at the bottom.
** Sorry could one of the moderators please move this thread to the Help me section**